The treatment of infants infected with HIV early in life with antiretroviral agents may prevent the early and rapid decline of CD4s and immune function and, therefore, decrease the overall morbidity and mortaliity in this group of in fants. This is a two-part, multicenter, phase I/II study. Part A will determine the safety, tolerance and pharmacokinetics of the combination of ddI with ZDV, in HIV-infected infants or exposed infants on ZDV<120 days of age. Part B is a phase II study of ddI alone vs ZDV and ddI in infants enrolled <90days old.